Basis set Slater

H is the one-electron operator and i is the Slater basis set function (2s, 2p). The diagonal elements of Htj (Hit) are approximated as the valence state ionization potentials and the off-diagonal elements Htj are estimated using the Wolfsberg-Helmholtz approximation,... 

McLean, A. D., and McLean, R. S. (1981). Roothaan-Hartree-Fock atomic wavefunctions. Slater basis set expansions for A=55-92. Atomic Data and Nuclear Data Tables 26, 197-401. 

Clearly, this approach can also be used in the case of Slater basis sets and, moreover, in the case of universal Slater basis sets. Ruedenberg and co-workers104 105 have shown that, within the molecular orbital approximation, this systematic approach gives a series of energy values which smoothly approach the Hartree-Fock limit. Similarly smooth convergence is to be expected in the calculation of correlated wave functions and expectation values, and will be the subject of future studies in this area.106... 

To summarize the discussion, the Gaussian and Slater basis sets of the same size and quality give comparable energies and the other molecular properties. 

Table II shows that Simons basis set (set I) reproduces the experimental values rather accurately for the and 2 ionization potentials, the errors being 0.14 and 0.22 eV, respectively. These results represent vast improvements over the Koopmans theorem values of 17.58 and 21.75 eV. However, the n state is grossly in error, being 1.11 eV different from experiment. (Simons, at first, mistakenly reported his value to be 1 eV lower than this, leading him to conclude, erroneously, that the EOM method gave accurate IPs for all three states with this basis set. ) Adding the polarization functions to Simons basis set (giving basis set II) lowers the calculation of the troublesome IP by 0.36 eV and leaves the other states relatively unaffected. The EOM results with Nesbet s basis (set III) are much better still all the IPs are within 0.34 eV of experiment. The calculations employing basis set IV indicate that the EOM Gaussian basis set calculations are of comparable accuracy to the double zeta Slater basis sets with polarization functions. ...

The variational treatment of the ground states of point-nuclear hydrogenic ions using a minimal Slater basis set is familiar to every student of quantum chemistry. If we work with the radially reduced Schrodinger equation, the trial function, rpr has the form... 

The theoretical chemistry community developed density functional theory for finite molecular systems which involve molecules and cluster models that describe the catalytic systems. They use the same constructs used in many ab initio wavefunction methods, i.e. Gaussian or Slater basis sets. The solid-state physics community, on the other hand, developed density functional theory to describe bulk solid-state systems and infinite surfaces by using a supercell approach along with periodic basis functions, i.e. plane waves . Nearly all of our discussion has focused on finite molecular systems. In the next section we will describe in more detail infinite periodic systems. 

M. Towler, An introductory guide to Gaussian basis sets in solid state electronic structure calculations, http //www.orystal.unito.it/tutojan2004/tutorials/index.html A.D. McLean, R.S. McLean, Roothaan-Hartree-Fock atomic wave functions (Slater basis-set expansions for Z=55-92),... 

The STO basis set of the DZ type ean be approximated by split polynomials of the Gaussian-type functions M-NP G. Each inner AO is replaced by M GTO orbitals, the valence 2s orbital—by AT, while the p orbital—by P GTO functions. For example, the 4-31 G basis set describes every inner (Is) orbital by four GTO s, every valence 2s AO by three GTO s and every valence p AO by one GTO. It is important to point out that whereas in the case of the minimal basis set of the NG type the accuracy level of the minimal STO basis set cannot be attained even at great values of N, the use of the split-valence GTO M-NPG basis sets allows the Slater basis set level to be exceeded. 

Table 19.1 Ground-state energy Eq, first excited-state energy E, and vertical excitation energy E — Eo for the singlet n —f n transition in the acrolein molecule at the experimental geometry calculated in DMC with different time steps % using the VBl Slater basis set and a state-specific Jastrow-Slater CAS(6,5) wave function with Jastrow, CSF and orbital parameters optimized by energy minimization in VMC...

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